To address core challenges such as resource constraints on edge devices, data privacy concerns, and poor translation quality for low-resource languages, this paper proposes a Multitask Bayesian Federated Learning (MT-BayesFL) framework to achieve efficient, robust, and trustworthy multilingual translation while preserving data locality. The framework's core is multi-task collaboration. Through a lightweight shared encoder and task-specific decoder architecture, the framework enables the natural transfer of general semantic knowledge learned in high-resource languages to low-resource languages via the shared encoder, directly alleviating the data sparsity problem and achieving mutual benefit between tasks.